What is the integral of 3x^2cos(x^3) ?

The integral of 3x^2cos(x^3) is sin(x^3)+C

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integral of 3x^2cos(x^3)

\int 3 x^{2} cos (x^{3}) d x

sin (x^{3}) + C

Solution steps

\int 3 x^{2} cos (x^{3}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{2} cos (x^{3}) d x

Apply u-substitution

: \int \frac{cos ( u )}{3} d u

= 3 \cdot \int \frac{cos ( u )}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 3 \cdot \frac{1}{3} sin (u)

Substitute back

u = x^{3}

= 3 \cdot \frac{1}{3} sin (x^{3})

Simplify

3 \cdot \frac{1}{3} sin (x^{3}) : sin (x^{3})

= sin (x^{3})

Add a constant to the solution

= sin (x^{3}) + C

f (x) = 5 e^{4 x}

x \frac{d y}{d x} + 2 y = - 3 e^{x}

\frac{d}{d x} (7 - 4 x)

\int 2 x^{- 4} d x

sin (x^{2} + 1)

What is the integral of 3x^2cos(x^3) ?
The integral of 3x^2cos(x^3) is sin(x^3)+C